The current hardware equipment used to detect the content of each element component in the rare earth extraction process has a complex structure and high maintenance cost. A modeling method for the soft measurement of rare earth multi-element component content is proposed to address this issue. This method uses the Multi-LightVGG multi-tasking learning model and the Multi Gradient Descent Algorithm based on Optimized Upper Bound (MGDA-OUB) to optimize the model for each prediction task and find the Pareto optimal solution. After conducting several experiments, the Multi-LightVGG model loaded with MGDA-OUB has lower MRE, RMSE for Pr, Nd prediction, and MAX(|error|) for Nd prediction than the Multi-LightVGG model without MGDA-OUB by 0.3778%, 0.5208%, 0.0015, 0.0015, and 0.1985%, respectively; and the MRE and RMSE of the Multi-LightVGG model for Pr and Nd prediction under the same optimization conditions are lower than those of Multi-ResNet18 by 0.3297%, 0.5423%, 0.0019, and 0.002, respectively, thus indicating that MGDA-OUB can effectively solve multiple task-specific Pareto solutions to avoid possible conflicts between specific tasks, while the Multi-LightVGG model, compared to the Multi-Resnet18 model, has a backbone network that can effectively capture the abstract representations in the images of the rare earth-extraction mixed solution, which in turn improves the prediction accuracy of the content of each elemental component.